Pompeo also told Moon that Kim agreed to meet with Trump at a summit that "should be held as soon as possible," according to a statement the South Korean leader's office issued later.

Moon's office also indicated that the U.S. and North Korea are still discussing when and where the meeting will be held.

Trump, meanwhile, said in a tweet that he looks forward to seeing Kim in the "near future."

.@SecPompeo had a good meeting with Chairman Kim today in Pyongyang. Progress made on Singapore Summit Agreements! I look forward to seeing Chairman Kim again, in the near future. pic.twitter.com/bUa2pkq80s